Facebook allows you to create and participate in groups. Groups all have their own rules within Facebook, and are run by other Facebook members. They are rarely policed by Facebook, and are instead designed around self-managed communities.
Groups are an effective marketing tool when used correctly.
You create groups connected to your profile or page. When managed from a page, they are relatively anonymous – when managed from your personal profile, they are connected to your name. It’s your choice how you manage them.
You can only currently join groups using your profile, not your page.